x根号y-y根号x/x根号y+y根号x-y根号x+x根号y/y根号x-x根号y=急求,救命啊

题目

x根号y-y根号x/x根号y+y根号x-y根号x+x根号y/y根号x-x根号y=急求,救命啊

答案

[(x√y-y√x)/(x√y+y√x)]-[(y√x+x√y)/(y√x-x√y)]
=[(√x-√y)/(√x+√y)]-[(√y+√x)/(√y-√x)] 这一步是两分式分子分母分别同除以√(xy)
=[(√x-√y)²/(x-y)]-[(√x+√y)²/(y-x)]
=[(√x-√y)²+(√x+√y)²]/(x-y)
=(2x+2y)/(x-y)
=2(x+y)/(x-y)